reserve S,S9 for non void Signature,
  f,g for Function;

theorem Th51:
  for S,T being Signature st S is empty holds T is Extension of S
proof
  let S, T be Signature;
  assume
A1: the carrier of S is empty;
  then the carrier' of S = {} by INSTALG1:def 1;
  then the Arity of S = {};
  then
A2: the Arity of S c= the Arity of T;
  the ResultSort of S = {} by A1;
  then the ResultSort of S c= the ResultSort of T;
  hence S is Subsignature of T by A1,A2,INSTALG1:13,XBOOLE_1:2;
end;
